Lecture 3 - Carnot Cycle Flashcards
How is the SFEE written for boilers and condensers, and why?
DetlaQ = h2-h1
They do no work on the fluid
How is the simplified SFEE written for turbines and compressors, and why?
-DeltaW = (h2-h1)
Kinetic energy changes are negligible so neglected
Processes are adiabatic (no heat transfer)
What equation can be used on a perfect gas in a turbine or compressor?
(Give rearranged version too)
cp = (dh/dT)p
Can also be written as
h2-h1 = cp(T2-T1)
How is the SFEE written for nozzles and diffusers?
(0.5C2^2-0.5C1^2) = (h1-h2)
Why can’t kinetic energy be neglected in the SFEE for nozzles and diffusers?
In these devices they may become significant terms
Why does the Carnot cycle accept heat at one max temp and reject it at a fixed lower temp?
The larger the average temperature difference, the greater the efficiency of the cycle. This system maintains the highest difference.
Which components are involved in the Carnot cycle?
Pump, boiler, turbine, condenser
What is required for an ideal thermodynamic cycle in the Carnot cycle?
Reversible isothermal processes
Reversible adiabatic processes (compression and expansion) - ie isentropic process
How would an ideal thermodynamic cycle be achieved in the Carnot cycle?
Using a fluid which is a condensable vapour.
Isothermal processes carried out at constant pressure and temperature, working fluid changes state
On a T-s diagram,, what are
4-1, 1-2, 2-3, 3-4?
4-1: pump, isentropic
1-2: boiler, isothermal
2-3: turbine, isentropic
3-4: condenser, isothermal
Give the SFEE for all processes of the Carnot cycle
Boiler: Q1-2 = h2-h1
Turbine: W2-3 = h3-h2
Condenser: Q3-4 = h4-h3
Pump: W4-1 = h4-h1
What is represented by:
T, s, h, Q, W, cp, U?
T = Temperature s = entropy h = enthalpy Q = heat transferred W = work transferred U = internal energy
How is an ideal component’s thermodynamic state designated?
By a prime (ie 1’ for position 1) next to the actual numerical value on the graph
How does entropy change in ideal vs non-ideal fluid processes?
Ideal: no change
Non-ideal: increases
The higher the value of X, the more efficient the cycle.
What is X?
The maximum temperature
What is the temperature at which heat is rejected from the cycle at governed by?
Atmospheric considerations, ie temp difference between working fluid and sink
What is the maximum working temperature of the Carnot cycle governed by?
Strength of materials- must be able to withstand pressures
Why can the Carnot cycle not make the best use of material limits?
To operate in the wet region, the temp is limited to critical temp, 374C, whereas the materials can withstand 550-600C.
What are the problems with using a mixture of liquid and vapour?
Impossible to get pump that works on two phase fluid
Liquid droplets can damage turbine blades due to high speeds
Draw a Ts diagram of a carnot cycle?
Square box
1) isothermal expansion
2) Adiabatic expansion
3) Isothermal Compression
4) Adiabatic Compression
Draw a pressure volume diagram of a carnot cycle?
1) isothermal expansion
2) Adiabatic expansion
3) Isothermal Compression
4) Adiabatic Compression
How can you determine the properties of the fluids at different points within the carnot cycle?
If on saturated line - either completely liquid or vapour
Isentropic process therefore entropy will be the same at inlet and outlet of turbine and at the inlet and outlet of pump
How can the wetness/dryness fraction initially be determined?
by using the known entropy of the fluid and calculating with the saturated entropy of the liquid and steam at that pressure
What is the net work output of the carnot cycle?
Energy out of turbine - energy into pump
h2 - h3) - (h1 - h4
What is the efficiency of the carnot cycle?
Net work out/Heat in or simplified to
Thot - Tcold / Thot
How are turbine and compressor efficiencies taken into account
for turbine - change in enthalpy * efficiency - get less work out
for compressor - change in enthalpy/efficiency - have to put more work in
